MONTPELIER — The Vermont House on Friday passed new and higher school taxes for the coming academic year, with some lawmakers saying they are hoping for big changes in the state’s school funding system in the coming years.

The bill raises the state-determined share of the residential property tax from 94 cents per $100 of property value to 98 cents per $100. Additional school taxes voted by local school districts bring the average rate on a homestead and up to 2 acres to an average of about $1.49, said Rep. Dave Sharpe, D-Addison, a member of the House Ways and Means Committee.

For nonresidential properties, such as vacation, commercial and rental properties, the statewide rate would go from $1.44 to $1.51 plus a half-cent per $100 of value. That’s a flat, statewide rate; local budget votes don’t affect it.

Supporters expressed relief that the tax increases were smaller than some projected over the winter. But opponents said more needs to be done to hold down rising education costs in a time of declining student enrollment.

“This bill once again nibbles around the edges but does not address the real problem of unsustainable increases in education costs,” said House Minority Leader Don Turner, R-Milton.

The bill contains some ambitious plans for the future. It calls for the Legislature to adopt by 2017 a package of significantly lower residential property taxes, achieved by shifting some education costs onto a new income tax, which would be added to the state income tax already in place.

In Vermont’s complex school funding system, the statewide tax rates are influenced by local budget decisions. Sen. Tim Ashe, chairman of the Senate Finance Committee, said when the school tax bill moves to the Senate it could be adjusted again, depending on what happens with some still undecided local school budgets.

Thirty-five local districts turned down their school boards’ budget requests last month, including in the capital, Montpelier, and in the largest city, Burlington. District boards have been working to craft trimmed-down spending plans.

Ashe, who ran on a Democrat-Progressive fusion ticket, said the 35 budgets, out of nearly 250 around the state, represent about 25 percent of Vermont students.

The House’s final passage of its school tax bill came after heated debate that took up much of Thursday and Friday. On Friday, House members rejected a move by Rep. Kurt Wright, R-Burlington, to put new controls on the costs imposed on local schools by the state by voting for a less tough substitute amendment.

Wright’s amendment would have required that the cost of what he termed “unfunded mandates” issued by the state be calculated on a yearly basis and that the money be paid out of the state’s general fund.

Sharpe successfully offered a substitute amendment requiring the costs to be calculated but stopped short of saying the state would pay them.